论文标题
具有理性符号的无界Toeplitz操作员
Unbounded Toeplitz Operators with Rational Symbols
论文作者
论文摘要
详细分析了无界（和有限的）Toeplitz运算符（TO），表明它们是密集定义的闭合，并具有有限的尺寸内核和缺陷空间。后一个空间以及域，范围，光谱和弗雷德霍尔姆点。特别是，在对称情况下，即对于实际有理符号，缺乏空间和索引可明确可用。 总结部分简要概述了无限制的研究，以找到当前的贡献。关于一般不受限制的属性，它提供了一些新的结果，以回忆起与维纳 - hopf运营商的密切关系，并且在半充电的情况下，与希尔伯特转换类型的单一操作员相关。文献中考虑的特定符号承认进一步分析。对于半曲线和真实的正方形综合符号，得出了一些结论。有一种半弯曲的方法，该方法从与Toeplitz矩阵有关的紧密的半圆形形式开始。研究了与此类形式相关的friedrichs扩展。最后，简要检查了对类似于和toeplitz的运算符的分析，这通常与此处的处理不同。
Unbounded (and bounded) Toeplitz operators (TO) with rational symbols are analysed in detail showing that they are densely defined closed and have finite dimensional kernels and deficiency spaces. The latter spaces as well as the domains, ranges, spectral and Fredholm points are determined. In particular, in the symmetric case, i.e., for a real rational symbol the deficiency spaces and indices are explicitly available. The concluding section gives a brief overview on the research on unbounded TO in order to locate the present contribution. Regarding properties of unbounded TO in general, it furnishes some new results recalling the close relationship to Wiener-Hopf operators and, in case of semiboundedness, to singular operators of Hilbert transformation type. Specific symbols considered in the literature admit further analysis. Some conclusions are drawn for semibounded integrable and real square-integrable symbols. There is an approach to semibounded TO, which starts from closable semibounded forms related to a Toeplitz matrix. The Friedrichs extension of the TO associated with such a form is studied. Finally, analytic TO and Toeplitz-like operators are briefly examined, which in general differ from the TO treated here.
